© 2015 American Physical Society. We report a measurement of the B0 and B+ meson decays to the D-sK0Sπ+ and D-sK+K+ final states, respectively, using 657 × 106BB¯ pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e+ collider. Using the D-s → φ π-, K∗(892)0K- and K0SK- decay modes for the Ds reconstruction, we measure the following branching fractions: B(B0 → D-sK0sπ+) = [0.47 ± 0.06(stat) ± 0.05(syst)] × 10-4 and B(B+ → D-sK+K+) = [0.93 ± 0.22(stat) ± 0.10(syst)] × 10-5. We find the ratio of the branching fraction of B+ → D-sK+K+ to that of the analogous Cabibbo-favored B+ → D-sK+π+ decay to be RB = 0.054 ± 0.013(stat) ± 0.006(syst), which is consistent with the naive factorization model. We also observe a deviation of the DsK invariant-mass distribution from the three-body phase-space model for both studied decays.